Hi I'm planning to setup a private ethereum network. So my doubt is, since my network is private, Is it possible to get real ether whose value can be exchanged for real money? Or private network in only for testing or something like that. I have read that private networks can also be useful for mining.
Private networks are universes of their own. At protocol level your private network does not know about the existence of Ethereum (where real ETH exists).
Your private network ETH only exists in your private network. Real ETH does not interact, nor exist on your private network.
No, it's not possible. The value of the ether is defined by the supply demand curve and exchanged on trading platform that allows that.
So its worthless unless you create a new blockchain platform with a new crypto and you convince an exchange to trade it.
That's the same for the ethereum testing net and any private net you set it up locally. These are fork networks (not the main one) and the value of their ether is not traded, so it worth zero.
And, just to formalize it better, mining doesn't mean making money. The mining is also the way to secure the network by creating, verifying, publishing and propagating blocks in the blockchain and for this computational work the miner will get a reward (in form of eth) . ref
So yes, you mine also in a private network, but you don't get any reward. Or, better, the reward you get is worthless.